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When it comes to alternate current, a complex description is pretty common as it's apperently easier to calculate with. But I don't understand alternate current to be honest. I have a problem with the basics, especially the following:

I can describe alternate current with sine, for example:

[tex] I(t)=I_{0}*sin(\omega t)[/tex]

where I_0 is the max amplitude.

but I can also write an alternate current like this:

[tex] I(t)=I_{0}*e^{i \omega t} [/tex]

i=imaginary unit

but with Euler's formula I can reqrite this to:

[tex] I(t)=I_{0}*[cos(\omega t)+i*sin(\omega t)][/tex]

What does the imaginary part tells me here? Both equations express an alternate current, but they are different (to me at least:) )

I'm pretty sure I have a wrong imagination of this stuff. Can someone explain it to me? I hope you get the point where my problems are.

Thanks for your help in advance